10-bit two’s complement of -37 – UGC NET Question

To encode -37 in 10-bit two's complement, we first write +37 in binary as 0000100101₂. We then invert all bits to get 1111011010₂ and add 1, obtaining 1111011011₂. This pattern, when interpreted as a 10-bit two's complement number, represents -37. Hence, option C correctly represents -37.

Option A:
Option A corresponds to a different 10-bit pattern whose two's complement value is not -37. When interpreted as signed, its magnitude is larger and corresponds to another negative integer. Thus, it is not the correct encoding for -37.

Option B:
Option B also represents a negative number in 10-bit two's complement but its value differs from -37, as a different set of bits is set in the magnitude part. Therefore, it does not match the required decimal number.

Option C:
Option C is obtained by a standard two's complement procedure: writing +37, bitwise complementing, then adding 1. Its signed value is exactly -37, which can be confirmed by decoding it back to decimal. This makes it the unique correct representation among the given options.

Option D:
Option D again produces a negative number but with a different offset from 0 than -37. The positions of ones and zeros differ from the calculated two's complement of 37, so it does not represent -37.